This section provides background information related to the present disclosure that is not necessarily prior art. This section also provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.
According to the principles of the present teachings, methods are provided for forward and back-projection, which are referred to as separable footprint (SF) projectors: the SF-TR and SF-TT projectors being exemplary embodiments. These methods approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. In some embodiments, the SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction. In some embodiments, the SF-TT projector uses trapezoid functions in both the axial and transaxial directions. Simulations and experiments showed that both SF projector methods are more accurate than conventional distance-driven (DD) projectors. Moreover, the SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. In some embodiments, the SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.
Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.
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